The detergent breaks down the two sacks: cell membranes and the
nucleus. The enzymes in the soap break down the molecules and the
membranes and release the cell contents which include the DNA. Almost
all of the DNA is from the cell nucleus.

To one of my experiments I added a pinch of meat tenderizer. This
product contains enzymes which are also proteins. Proteins help break
up the cell membrane.

The isopropyl alcohol does not dissolve the DNA which floats up to
the top. The material at the bottom of the test tube is cell scum.